Finite Group Databasebeta

← #14726327

Subgroups — #14726327

Order 2816.

904 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078742C212yesmaximal, complemented
2#13074193C211yesmaximal, characteristic
3#13067624C212yesmaximal, complemented
4#13067607C212yesmaximal
5#13067590C212yesmaximal, complemented
6#13067573C212yesmaximal
7#13067167C212yesmaximal, complemented
8#13066950C211yesmaximal, characteristic
9C11×#3458C211yesmaximal, characteristic
10C11×#544—22no—
11C11×#544—22no—
12C11×#544—21no—
13C11×#544C2212yes—
14C11×#543—21no—
15C11×#543C2212yes—
16C11×#533—24no—
17C11×#533—21no—
18C11×#533C2212yes—
19C2×C11×#117—21no—
20C2×C11×#117C2211yescharacteristic
21C2×C4×Dic22C2211yescharacteristic
22#10622823—21no—
23#10622707—22no—
24#10622703—22no—
25#10622663C2214yes—
26#10622656C2214yes—
27#10622643—24no—
28#10622596C2211yescharacteristic
29#10622592C2211yescharacteristic
30#10622591—21no—
31#10622566C2211yescharacteristic
32#10622560C2211yescharacteristic
33#10622557—21no—
34#10622550C2211yescharacteristic
35#10622546—21no—
36#10622539C2212yes—
37#10622176C2214yes—
38#10622176C2214yes—
39#10622166C2212yes—
40#10622163C2212yes—
41C23×C4×C11D411yescharacteristic
42C22×Dic22C2311yescharacteristic
43C11×C4⋊Q8—24no—
44C11×C4⋊Q8—21no—
45C11×C4⋊Q8—21no—
46C11×C4⋊Q8—24no—
47C11×C4⋊Q8D412yes—
48C11×C4⋊Q8D412yes—
49C11×#125—24no—
50C11×#125—22no—
51C11×#125—24no—
52C11×#125—22no—
53C11×C22⋊Q8—24no—
54C11×C22⋊Q8—24no—
55C11×C22⋊Q8—24no—
56C11×C22⋊Q8—22no—
57C11×C22⋊Q8—22no—
58C11×C22⋊Q8—22no—
59C11×C22⋊Q8—24no—
60C11×C22⋊Q8C2314yes—
61C4×Q8×C11—22no—
62C4×Q8×C11—22no—
63C4×Q8×C11—22no—
64C4×Q8×C11D414yes—
65C11×#117—22no—
66C11×#117—22no—
67C11×#117—22no—
68C11×#117—22no—
69C11×#117—22no—
70C11×#117—22no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4D411yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C22⋊C4—22no—
76C2×C11×C22⋊C4D411yescharacteristic
77C2×C11×C22⋊C4C2311yescharacteristic
78C2×C42×C11—22no—
79C2×C42×C11D411yescharacteristic
80C2×C42×C11C2311yescharacteristic
81C2×C22⋊Dic11—21no—
82C2×C22⋊Dic11—21no—
83C2×#4326—24no—
84C2×C4⋊Dic11C2311yescharacteristic
85C2×Dic11⋊C4—21no—
86C2×Dic11⋊C4—21no—
87C2×Dic11⋊C4—21no—
88C2×C4×Dic11—21no—
89C4×Dic22—22no—
90C4×Dic22—22no—
91#66899—24no—
92C11⋊#95—21no—
93C11⋊#95—21no—
94C11⋊#95—21no—
95C11⋊#95—21no—
96C11⋊#95—21no—
97C11⋊#95—21no—
98C11⋊#95C2311yescharacteristic
99C11⋊#95C2311yescharacteristic
100C22⋊(C11⋊C8)C2314yes—
101#66874—24no—
102#66872—24no—
103C4⋊(C11⋊C8)—22no—
104#66867—22no—
105#18155—111nomaximal, Sylow
106C24×C11C2×D411yescharacteristic
107C2×Q8×C11—22no—
108C2×Q8×C11—22no—
109C2×Q8×C11—22no—
110C2×Q8×C11C2×D414yes—
111C22×C4×C11—22no—
112C22×C4×C11—21no—
113C22×C4×C11—21no—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11C2×D411yescharacteristic
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2411yescharacteristic
123C22×Dic11—21no—
124C22×Dic11—21no—
125C22×Dic11—21no—
126C22×Dic11—21no—
127C2×Dic22—22no—
128C2×Dic22—42no—
129C11×C4⋊C4—22no—
130C11×C4⋊C4—22no—
131C11×C4⋊C4—22no—
132C11×C4⋊C4—24no—
133C11×C4⋊C4—24no—
134C11×C4⋊C4—22no—
135C11×C4⋊C4—22no—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4—22no—
139C11×C4⋊C4—24no—
140C11×C4⋊C4—22no—
141C11×C4⋊C4—24no—
142C11×C4⋊C4C2×D414yes—
143C11×C22⋊C4—24no—
144C11×C22⋊C4—24no—
145C11×C22⋊C4—22no—
146C11×C22⋊C4—22no—
147C42×C11—24no—
148C42×C11—24no—
149C42×C11—21no—
150C42×C11—21no—
151C42×C11C2×D412yes—
152C42×C11C2×D412yes—
153C22⋊Dic11—42no—
154C22⋊Dic11—42no—
155#4326—48no—
156C4⋊Dic11—22no—
157Dic11⋊C4—42no—
158Dic11⋊C4—41no—
159Dic11⋊C4—41no—
160Dic11⋊C4—42no—
161C4×Dic11—42no—
162C2×C11⋊C8—24no—
163#3458D1111yescharacteristic
164#3113—112no—
165#2599—111no—
166#1611—112no—
167#1608—112no—
168#1605—112no—
169#1602—112no—
170#1515—112no—
171#1464—111no—
172C23×C11—21no—
173C23×C11—21no—
174C23×C11—41no—
175C23×C11—41no—
176C23×C11#13712yes—
177C23×C11C22×D411yescharacteristic
178Q8×C11—44no—
179Q8×C11—82no—
180Q8×C11—82no—
181Q8×C11—82no—
182C2×C4×C11—24no—
183C2×C4×C11—24no—
184C2×C4×C11—21no—
185C2×C4×C11—21no—
186C2×C4×C11—21no—
187C2×C4×C11—21no—
188C2×C4×C11—24no—
189C2×C4×C11—21no—
190C2×C4×C11—21no—
191C2×C4×C11—24no—
192C2×C4×C11—41no—
193C2×C4×C11—41no—
194C2×C4×C11—41no—
195C2×C4×C11—41no—
196C2×C4×C11—82no—
197C2×C4×C11—82no—
198C2×C4×C11#12012yes—
199C2×C4×C11#12011yescharacteristic
200C2×C4×C11#12011yescharacteristic
201C2×C4×C11#13712yes—
202C2×C4×C11C22×D412yes—
203C2×Dic11—22no—
204C2×Dic11—41no—
205C2×Dic11—41no—
206C2×Dic11—41no—
207C2×Dic11—41no—
208C2×Dic11—41no—
209C2×Dic11—41no—
210C2×Dic11—41no—
211C2×Dic11—41no—
212C2×Dic11—41no—
213C2×Dic11—41no—
214C2×Dic11—41no—
215Dic22—24no—
216Dic22—42no—
217C11⋊C8—44no—
218#544—22no—
219#544—22no—
220#544—21no—
221#544C2×D1112yes—
222#543—21no—
223#543C2×D1112yes—
224#533—24no—
225#533—21no—
226#533C2×D1112yes—
227C2×C4×Q8—111no—
228C2×#117—21no—
229C2×#117C2×D1111yescharacteristic
230#483—114no—
231#475—222no—
232#462—222no—
233#451—114no—
234#441—224no—
235#432—112no—
236#398—111no—
237#397—111no—
238#395—111no—
239#393—111no—
240#388—221no—
241#387—221no—
242#387—221no—
243#385—221no—
244#383—111no—
245#328—114no—
246#328—114no—
247#324—112no—
248#323—112no—
249C22×C11—21no—
250C22×C11—21no—
251C22×C11—22no—
252C22×C11—42no—
253C22×C11—41no—
254C22×C11—41no—
255C22×C11—81no—
256C22×C11C2×#12011yescharacteristic
257C22×C11C2×#13711yescharacteristic
258C22×C11C2×#13711yescharacteristic
259C4×C11—21no—
260C4×C11—21no—
261C4×C11—22no—
262C4×C11—22no—
263C4×C11—22no—
264C4×C11—41no—
265C4×C11—44no—
266C4×C11—41no—
267C4×C11—44no—
268Dic11—42no—
269Dic11—81no—
270Dic11—81no—
271Dic11—81no—
272C22×Q8—111no—
273C23×C4C22⋊D1111yescharacteristic
274C2×Q16—224no—
275C4⋊Q8—24no—
276C4⋊Q8—21no—
277C4⋊Q8—21no—
278C4⋊Q8—24no—
279C4⋊Q8C22⋊D1112yes—
280C4⋊Q8C22⋊D1112yes—
281#125—24no—
282#125—22no—
283#125—24no—
284#125—22no—
285C22⋊Q8—24no—
286C22⋊Q8—24no—
287C22⋊Q8—24no—
288C22⋊Q8—22no—
289C22⋊Q8—22no—
290C22⋊Q8—22no—
291C22⋊Q8—24no—
292C22⋊Q8C22×D1114yes—
293C4×Q8—22no—
294C4×Q8—22no—
295C4×Q8—22no—
296C4×Q8—222no—
297C4×Q8—222no—
298C4×Q8C22⋊D1114yes—
299#117—22no—
300#117—22no—
301#117—22no—
302#117—22no—
303#117—22no—
304#117—22no—
305C2×C4⋊C4—21no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—111no—
308C2×C4⋊C4—221no—
309C2×C4⋊C4—221no—
310C2×C4⋊C4—221no—
311C2×C4⋊C4C22⋊D1111yescharacteristic
312C2×C4⋊C4C22×D1111yescharacteristic
313C2×C22⋊C4—22no—
314C2×C22⋊C4—221no—
315C2×C22⋊C4—221no—
316C2×C22⋊C4C22⋊D1111yescharacteristic
317C2×C22⋊C4C22×D1111yescharacteristic
318C2×C42—22no—
319C2×C42—221no—
320C2×C42C22⋊D1111yescharacteristic
321C2×C42C22×D1111yescharacteristic
322#106—224no—
323C4⋊C8—222no—
324#103—224no—
325#103—224no—
326C22⋊C8—114no—
327#97—222no—
328#95—111no—
329#95—111no—
330#95—221no—
331#95—221no—
332#95—221no—
333#95—221no—
334#95—221no—
335#95—221no—
336C2×C11—21no—
337C2×C11—21no—
338C2×C11—42no—
339C2×C11#300411yescharacteristic
340C2×C11#302211yescharacteristic
341C2×C11#302511yescharacteristic
342C24C2×C22⋊D1111yescharacteristic
343C2×Q8—22no—
344C2×Q8—22no—
345C2×Q8—22no—
346C2×Q8—222no—
347C2×Q8—442no—
348C2×Q8C2×C22⋊D1114yes—
349C22×C4—22no—
350C22×C4—22no—
351C22×C4—21no—
352C22×C4—21no—
353C22×C4—22no—
354C22×C4—22no—
355C22×C4—221no—
356C22×C4—221no—
357C22×C4—221no—
358C22×C4—221no—
359C22×C4C2×C22⋊D1111yescharacteristic
360C22×C4C2×C22⋊D1111yescharacteristic
361C22×C4C2×C22⋊D1111yescharacteristic
362C22×C4C2×C22⋊D1111yescharacteristic
363C22×C4C2×C22⋊D1111yescharacteristic
364C22×C4C23×D1111yescharacteristic
365Q16—448no—
366C2×C8—224no—
367C4⋊C4—22no—
368C4⋊C4—22no—
369C4⋊C4—22no—
370C4⋊C4—24no—
371C4⋊C4—24no—
372C4⋊C4—22no—
373C4⋊C4—22no—
374C4⋊C4—22no—
375C4⋊C4—22no—
376C4⋊C4—22no—
377C4⋊C4—24no—
378C4⋊C4—22no—
379C4⋊C4—24no—
380C4⋊C4—222no—
381C4⋊C4—442no—
382C4⋊C4—442no—
383C4⋊C4—441no—
384C4⋊C4—441no—
385C4⋊C4C2×C22⋊D1114yes—
386C22⋊C4—24no—
387C22⋊C4—24no—
388C22⋊C4—22no—
389C22⋊C4—22no—
390C22⋊C4—442no—
391C22⋊C4—442no—
392C42—24no—
393C42—24no—
394C42—21no—
395C42—21no—
396C42—442no—
397C42C2×C22⋊D1112yes—
398C42C2×C22⋊D1112yes—
399C11#1815511yescharacteristic, complemented, Sylow
400C23—21no—
401C23—21no—
402C23—41no—
403C23—41no—
404C23#6699512yes—
405C23C22×C22⋊D1111yescharacteristic
406Q8—44no—
407Q8—82no—
408Q8—82no—
409Q8—82no—
410Q8—224no—
411Q8—442no—
412C2×C4—24no—
413C2×C4—24no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—24no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—24no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—82no—
427C2×C4—82no—
428C2×C4—222no—
429C2×C4—441no—
430C2×C4—441no—
431C2×C4—441no—
432C2×C4—441no—
433C2×C4—441no—
434C2×C4—441no—
435C2×C4—441no—
436C2×C4—441no—
437C2×C4—441no—
438C2×C4—441no—
439C2×C4—441no—
440C2×C4#6699512yes—
441C2×C4#6700611yescharacteristic
442C2×C4#6700611yescharacteristic
443C2×C4#6700612yes—
444C2×C4C22×C22⋊D1112yes—
445C8—444no—
446C22—21no—
447C22—21no—
448C22—22no—
449C22—42no—
450C22—41no—
451C22—41no—
452C22—81no—
453C22C2×#6699511yescharacteristic
454C22C2×#6699511yescharacteristic
455C22C2×#6700611yescharacteristic
456C4—22no—
457C4—21no—
458C4—21no—
459C4—22no—
460C4—22no—
461C4—41no—
462C4—44no—
463C4—41no—
464C4—44no—
465C4—442no—
466C4—881no—
467C4—881no—
468C4—881no—
469C2—21no—
470C2—21no—
471C2—42no—
472C2#1307785011yescharacteristic
473C2#1307799511yescharacteristic
474C2#1307800811yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#3458C2
socleC22×C11C2×#120
prime radicalC24×C11C2×D4
hypercenter#3458D11
hypocenterC11#18155
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3458

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #13078742C2semidirect
3. #13067624C2semidirect
5. #13067590C2semidirect
7. #13067167C2semidirect
399. C11#18155semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#130787422
#130741932
#130676242
#130676072
#130675902
#130675732
#130671672
#130669502
C11×#34582
#1815511